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Research Papers

Disturbance Accommodating Control Design for Wind Turbines Using Solvability Conditions

[+] Author and Article Information
Na Wang

National Renewable Energy Laboratory,
15013 Denver West Parkway,
Golden, CO 80401
e-mail: na.wang@nrel.gov

Alan D. Wright

National Renewable Energy Laboratory,
15013 Denver West Parkway,
Golden, CO 80401
e-mail: alan.wright@nrel.gov

Mark J. Balas

Professor
Fellow ASME
Aerospace Engineering Department,
Embry-Riddle Aeronautical University,
Daytona Beach, FL 32114
e-mail: balasm@erau.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 29, 2016; final manuscript received October 5, 2016; published online February 7, 2017. Assoc. Editor: Ryozo Nagamune.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Dyn. Sys., Meas., Control 139(4), 041007 (Feb 07, 2017) (11 pages) Paper No: DS-16-1065; doi: 10.1115/1.4035097 History: Received January 29, 2016; Revised October 05, 2016

In this paper, solvability conditions for disturbance accommodating control (DAC) have been discussed and applied on wind turbine controller design in above-rated wind speed to regulate rotor speed and to mitigate turbine structural loads. An asymptotically stabilizing DAC controller with disturbance impact on the wind turbine being totally canceled out can be found if certain conditions are fulfilled. Designing a rotor speed regulation controller without steady-state error is important for applying linear control methodology such as DAC on wind turbines. Therefore, solvability conditions of DAC without steady-state error are attractive and can be taken as examples when designing a multitask turbine controller. DAC controllers solved via Moore–Penrose Pseudoinverse and the Kronecker product are discussed, and solvability conditions of using them are given. Additionally, a new solvability condition based on inverting the feed-through D term is proposed for the sake of reducing computational burden in the Kronecker product. Applications of designing collective pitch and independent pitch controllers based on DAC are presented. Recommendations of designing a DAC-based wind turbine controller are given. A DAC controller motivated by the proposed solvability condition that utilizes the inverse of feed-through D term is developed to mitigate the blade flapwise once-per-revolution bending moment together with a standard proportional integral controller in the control loop to assist rotor speed regulation. Simulation studies verify the discussed solvability conditions of DAC and show the effectiveness of the proposed DAC control design methodology.

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References

Figures

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Fig. 1

3DOF wind turbine model with two first blade flapwise modes and one rotor rotational mode. Ω is the rotor speed. (a) β is the collective pitch angle, and v is the uniform wind speed across the rotor plane. (b) β1,β2 are the independent pitch angles for each blade, y1, y2 are the blade flapwise bending moment for each blade, and v1, v2 are the wind speeds at the blade tips along the prevailing wind direction.

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Fig. 2

The uniform stepwise wind responses of the DAC-based CPCs solved via the Moore–Penrose Pseudoinverse and the Kronecker product, respectively, in terms of rotor speed Ω and pitch angle β. The stepwise wind is stepping from 17 m/s to 18 m/s at 50 s and then to 19 m/s at 100 s. There is regulated rotor speed error in the case of the Moore–Penrose Pseudoinverse (dashed curve) when the wind speed is drifting from the operating point at 18 m/s.

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Fig. 3

Uniform wind field with linear vertical shear. Wind speed v1, v2 at each blade tip are sinusoidal signals with rotor rotation. vd is the differential wind component, which is a sinusoidal signal. vc is the collective wind component, which is a constant speed.

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Fig. 4

The 10-min TurbSim-generated wind profiles with a mean of 18 m/s and a power law shear of 0.125. Including the wind speeds v1, v2 at each blade tip rotating with the rotor (top row), the differential component vd (middle row), and the collective wind component vc (bottom row). The PSDs for the corresponding wind components are included on the right side.

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Fig. 5

The turbulent wind responses of DAC IPC and DAC IPC with PI CPC in terms of the pitch actuator angles β1,β2, the rotor speed Ω, and the blade flapwise bending moments y1, y2 using the TurbSim-generated wind file as shown in Fig. 4. The segment from 300 s to 450 s is shown.

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Fig. 6

The PSDs of DAC IPC and DAC IPC with PI CPC in terms of the collective pitch component βc, the differential pitch component βd, the rotor speed Ω, the symmetrical blade flapwise bending moment ys, the asymmetrical blade flapwise bending moment yas, and the tower base fore-aft bending moment My using the TurbSim-generated wind file, as shown in Fig. 4

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